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Proof step 16 from proof bytes2int-rec (previous step)

(bytes2bits(bytes) + byte2bits(by)).first ⊦ bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by)) = [], bytes2bits(bytes) + byte2bits(by) = [], bytes = [], ~1 = bits2uint(bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by))) + bits2int(bytes2bits(bytes)) * 256 + band(b2i(by), 255)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first)
Proof step 18:
bytes2bits(bytes) ≠ [], bytes2bits(bytes).first ⊦ bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by)) = [], bytes2bits(bytes) + byte2bits(by) = [], bytes = [], ~1 = bits2uint(bitsinvert(bytes2bits(bytes)) + bitsinvert(byte2bits(by))) + bits2int(bytes2bits(bytes)) * 256 + band(b2i(by), 255)

Rule argument

seq: ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first) subst: [bits0, bits] → [byte2bits(by), bytes2bits(bytes)] rotate: F spec: list inst: bitlista name: first-01

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = []; Used terms: byte2bits(by), bytes2bits(bytes)